This has probably been posted before... but I was just wanting clarification on something. Is the first temp circled in the picture below core temp and the second one circled socket temp? I just wanted to be sure.

I assume I want to go by socket temp since apparently there is inaccuracy when it comes to internal temp readings for AMD cpus?

Sorry, but I don't know this for sure. It could be the socket temp or sampled temperature from the CPU with some correction factor. Only the mainboard manufacturer knows this for sure.
Try to put some load on the CPU and see how those values behave. Socket temperature should be changing slower that the internal.